Sparse-view x-ray computed tomography （CT） imaging is an interesting topic in CT field and can efficiently decrease radiation dose. Compared with spatial reconstruction, a Fourier-based algorithm has advantages in r...Sparse-view x-ray computed tomography （CT） imaging is an interesting topic in CT field and can efficiently decrease radiation dose. Compared with spatial reconstruction, a Fourier-based algorithm has advantages in reconstruction speed and memory usage. A novel Fourier-based iterative reconstruction technique that utilizes non-uniform fast Fourier transform （NUFFF） is presented in this work along with advanced total variation （TV） regularization for a fan sparse-view CT. The proposition of a selective matrix contributes to improve reconstruction quality. The new method employs the NUFFT and its adjoin to iterate back and forth between the Fourier and image space. The performance of the proposed algorithm is demonstrated through a series of digital simulations and experimental phantom studies. Results of the proposed algorithm are compared with those of existing TV-regularized techniques based on compressed sensing method, as well as basic algebraic reconstruction technique. Compared with the existing TV-regularized techniques, the proposed Fourier-based technique significantly improves convergence rate and reduces memory allocation, respectively.展开更多
For solving minimization problems whose objective function is the sum of two functions without coupled variables and the constrained function is linear, the alternating direction method of multipliers （ADMM） has exh...For solving minimization problems whose objective function is the sum of two functions without coupled variables and the constrained function is linear, the alternating direction method of multipliers （ADMM） has exhibited its efficiency and its convergence is well understood. When either the involved number of separable functions is more than two, or there is a nonconvex function~ ADMM or its direct extended version may not converge. In this paper, we consider the multi-block sepa.rable optimization problems with linear constraints and absence of convexity of the involved component functions. Under the assumption that the associated function satisfies the Kurdyka- Lojasiewicz inequality, we prove that any cluster point of the iterative sequence generated by ADMM is a critical point, under the mild condition that the penalty parameter is sufficiently large. We also present some sufficient conditions guaranteeing the sublinear and linear rate of convergence of the algorithm.展开更多
In ground-based astronomy, images of objects in outer space are acquired via ground-based tele- scopes. However, the imaging system is generally interfered by atmospheric turbulence and hence images so acquired are bl...In ground-based astronomy, images of objects in outer space are acquired via ground-based tele- scopes. However, the imaging system is generally interfered by atmospheric turbulence and hence images so acquired are blurred with unknown point spread function （PSF）. To restore the observed images, aberration of the wavefront at the telescope＇s aperture, i.e., the phase, is utilized to derive the PSF. However, the phase is not readily available. Instead, its gradients can be collected by wavefront sensors. Thus the usual approach is to use regularization methods to reconstruct high-resolution phase gradients and then use them to recover the phase in high accuracy. Here, we develop a model that reconstructs the phase directly. The proposed model uses the tight frame regularization and it can be solved efficiently by the Douglas-Rachford alternating direction method of multipliers whose convergence has been well established. Numerical results illustrate that our new model is efficient and gives more accurate estimation for the PSF.展开更多
基金Projected supported by the National High Technology Research and Development Program of China(Grant No.2012AA011603)the National Natura Science Foundation of China(Grant No.61372172)
文摘Sparse-view x-ray computed tomography （CT） imaging is an interesting topic in CT field and can efficiently decrease radiation dose. Compared with spatial reconstruction, a Fourier-based algorithm has advantages in reconstruction speed and memory usage. A novel Fourier-based iterative reconstruction technique that utilizes non-uniform fast Fourier transform （NUFFF） is presented in this work along with advanced total variation （TV） regularization for a fan sparse-view CT. The proposition of a selective matrix contributes to improve reconstruction quality. The new method employs the NUFFT and its adjoin to iterate back and forth between the Fourier and image space. The performance of the proposed algorithm is demonstrated through a series of digital simulations and experimental phantom studies. Results of the proposed algorithm are compared with those of existing TV-regularized techniques based on compressed sensing method, as well as basic algebraic reconstruction technique. Compared with the existing TV-regularized techniques, the proposed Fourier-based technique significantly improves convergence rate and reduces memory allocation, respectively.
文摘For solving minimization problems whose objective function is the sum of two functions without coupled variables and the constrained function is linear, the alternating direction method of multipliers （ADMM） has exhibited its efficiency and its convergence is well understood. When either the involved number of separable functions is more than two, or there is a nonconvex function~ ADMM or its direct extended version may not converge. In this paper, we consider the multi-block sepa.rable optimization problems with linear constraints and absence of convexity of the involved component functions. Under the assumption that the associated function satisfies the Kurdyka- Lojasiewicz inequality, we prove that any cluster point of the iterative sequence generated by ADMM is a critical point, under the mild condition that the penalty parameter is sufficiently large. We also present some sufficient conditions guaranteeing the sublinear and linear rate of convergence of the algorithm.
基金supported by Hong Kong Research Grants Council(HKRGC)(Grant Nos.CUHK400412 and HKBU203311)CUHK Direct Allocation Grant(Grant No.4053007)+1 种基金CUHK Focused Investment Scheme(Grant No.1902036)National Natural Science Foundation of China(Grant No.11301055)
文摘In ground-based astronomy, images of objects in outer space are acquired via ground-based tele- scopes. However, the imaging system is generally interfered by atmospheric turbulence and hence images so acquired are blurred with unknown point spread function （PSF）. To restore the observed images, aberration of the wavefront at the telescope＇s aperture, i.e., the phase, is utilized to derive the PSF. However, the phase is not readily available. Instead, its gradients can be collected by wavefront sensors. Thus the usual approach is to use regularization methods to reconstruct high-resolution phase gradients and then use them to recover the phase in high accuracy. Here, we develop a model that reconstructs the phase directly. The proposed model uses the tight frame regularization and it can be solved efficiently by the Douglas-Rachford alternating direction method of multipliers whose convergence has been well established. Numerical results illustrate that our new model is efficient and gives more accurate estimation for the PSF.
